It is well known from variational analysis (see, for instance,
[1]}, [2]}, [3]}, [4]}, [5]})
that distances from sublevel sets of a l.s.c. function can be
estimated in terms of its slope, while a certain positivity behaviour
of the slope allows one to establish solvability of inequalities.
All of this leads to investigate metric behaviours of the bifunction
\(f\) , which ensure these conditions to hold. The property
defined below pursues this purpose. It is a uniform variant
of a conceptual tool that was already considered in [5]},
in connection with the analysis of solvability and stability properties
of set-valued inclusions (see also [7]}).
